Information on Result #727211
Linear OA(27104, 750, F27, 51) (dual of [750, 646, 52]-code), using construction XX applied to C1 = C([721,42]), C2 = C([0,43]), C3 = C1 + C2 = C([0,42]), and C∩ = C1 ∩ C2 = C([721,43]) based on
- linear OA(2796, 728, F27, 50) (dual of [728, 632, 51]-code), using the primitive BCH-code C(I) with length 728 = 272−1, defining interval I = {−7,−6,…,42}, and designed minimum distance d ≥ |I|+1 = 51 [i]
- linear OA(2784, 728, F27, 44) (dual of [728, 644, 45]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 728 = 272−1, defining interval I = [0,43], and designed minimum distance d ≥ |I|+1 = 45 [i]
- linear OA(2798, 728, F27, 51) (dual of [728, 630, 52]-code), using the primitive BCH-code C(I) with length 728 = 272−1, defining interval I = {−7,−6,…,43}, and designed minimum distance d ≥ |I|+1 = 52 [i]
- linear OA(2782, 728, F27, 43) (dual of [728, 646, 44]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 728 = 272−1, defining interval I = [0,42], and designed minimum distance d ≥ |I|+1 = 44 [i]
- linear OA(276, 20, F27, 6) (dual of [20, 14, 7]-code or 20-arc in PG(5,27)), using
- discarding factors / shortening the dual code based on linear OA(276, 27, F27, 6) (dual of [27, 21, 7]-code or 27-arc in PG(5,27)), using
- Reed–Solomon code RS(21,27) [i]
- discarding factors / shortening the dual code based on linear OA(276, 27, F27, 6) (dual of [27, 21, 7]-code or 27-arc in PG(5,27)), using
- linear OA(270, 2, F27, 0) (dual of [2, 2, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(270, s, F27, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
Mode: Constructive and linear.
Optimality
Show details for fixed k and m, n and k, k and s, k and t, n and m, m and s, m and t, n and s, n and t.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Linear OOA(27104, 375, F27, 2, 51) (dual of [(375, 2), 646, 52]-NRT-code) | [i] | OOA Folding | |